Non-Gaussian Distributions in Extended Dynamical Systems

TL;DR

This paper introduces a new mechanism explaining the emergence of non-Gaussian tails in the probability distributions of local variables in nonlinear dynamical systems, supported by numerical evidence.

Contribution

It proposes a novel mechanism for non-Gaussian tails in PDFs of dynamical systems, supported by numerical simulations of passive scalar models.

Findings

Intermittent fluctuations can produce exponential tails in PDFs.

Numerical evidence supports the proposed mechanism.

Different PDF behaviors are outlined.

Abstract

We propose a novel mechanism for the origin of non-Gaussian tails in the probability distribution functions (PDFs) of local variables in nonlinear, diffusive, dynamical systems including passive scalars advected by chaotic velocity fields. Intermittent fluctuations on appropriate time scales in the amplitude of the (chaotic) noise can lead to exponential tails. We provide numerical evidence for such behavior in deterministic, discrete-time passive scalar models. Different possibilities for PDFs are also outlined.